Employing feedback in adiabatic quantum dynamics

TL;DR

This paper explores how feedback mechanisms influence quantum adiabatic dynamics, revealing deviations from traditional adiabatic theorem predictions and introducing a new gauge-invariant phase related to evolutionary game theory.

Contribution

It demonstrates that feedback alters adiabatic populations and introduces a novel gauge-invariant phase, expanding understanding of quantum adiabatic processes with feedback.

Findings

Feedback leads to non-constant adiabatic populations.

A new gauge-invariant adiabatic phase is identified.

The adiabatic theorem does not hold under feedback.

Abstract

We study quantum adiabatic dynamics, where the slowly moving field is influenced by system's state (feedback). The information for the feedback is gained from non-disturbating measurements done on an ensemble of identical non-interacting systems. The situation without feedback is governed by the adiabatic theorem: adiabatic energy level populations stay constant, while the adiabatic eigenvectors get a specific phase contribution (Berry phase). However, under feedback the adiabatic theorem does not hold: the adiabatic populations satisfy a closed equation of motion that coincides with the replicator dynamics well-known by its applications in evolutionary game theory. The feedback generates a new gauge-invariant adiabatic phase, which is free of the constraints on the Berry phase (e.g., the new phase is non-zero even for real adiabatic eigenfunctions).